Margenau on quadratic form

[fsonnichsen]

TL;DR Summary

From Margenau and Murphy--quadratic form use not clear

Looking at the proof of the Schwarz inequality in Margenau and Murphy, you will see what I attached. Gamma is asserted to be positive (OK). Given that the usual "quadratic form" solution would read "-(B+B*) .....". The sign does not seem correct to me as shown. In a fact B+B* = 2Re(B) and would be positive in this case given the integrals shown.
What am I missing here?

Thanks
Fritz

 

[BvU]

I think you found an error in the book. However, the values of $\lambda$ don't play a role in the argument (only the sign of the expression under the square root does), so I would call it a small error.

$\$

 

[fsonnichsen]

OK and thanks! The authors assumptions make sense but they must be evaluated carefully so I thought I may have missed something 49 years ago when I read the book the 1st time-it was quite a famous book back then.

I find the Cauchy-Schwarz ineq. for complex numbers in N dimensions somewhat tricky-the proof is not intuitively obvious to me upon brief examination.

Take care
Fritz